Question: Simplify the following expression: $ n = \dfrac{-7}{2} + \dfrac{-3p}{-4p - 9} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-4p - 9}{-4p - 9}$ $ \dfrac{-7}{2} \times \dfrac{-4p - 9}{-4p - 9} = \dfrac{28p + 63}{-8p - 18} $ Multiply the second expression by $\dfrac{2}{2}$ $ \dfrac{-3p}{-4p - 9} \times \dfrac{2}{2} = \dfrac{-6p}{-8p - 18} $ Therefore $ n = \dfrac{28p + 63}{-8p - 18} + \dfrac{-6p}{-8p - 18} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{28p + 63 - 6p}{-8p - 18} $ $n = \dfrac{22p + 63}{-8p - 18}$ Simplify the expression by dividing the numerator and denominator by -1: $n = \dfrac{-22p - 63}{8p + 18}$